Question: The sum of two numbers is $103$, and their difference is $83$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 103}$ ${x-y = 83}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 186 $ $ x = \dfrac{186}{2} $ ${x = 93}$ Now that you know ${x = 93}$ , plug it back into $ {x+y = 103}$ to find $y$ ${(93)}{ + y = 103}$ ${y = 10}$ You can also plug ${x = 93}$ into $ {x-y = 83}$ and get the same answer for $y$ ${(93)}{ - y = 83}$ ${y = 10}$ Therefore, the larger number is $93$, and the smaller number is $10$.